Fermi-liquid theory of the Korringa relations for the impurity-lattice relaxation of a pair of interacting Anderson impurities

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Abstract
We consider a pair of single-orbital Anderson impurities interacting with each other via a general two-body Hamiltonian. Using the Ward identities corresponding to the conservation of the total charge and the total spin, we derive the Korringa relations for the spin- and charge-lattice relaxation. The results are complementary to the Fermi-liquid relations for the specific heat, the charge, and spin susceptibilities derived previously. The results simplify in some special cases, i.e., two Kondo impurities, two nonmagnetic ions, a pair of mixed valence ions, the case of spinless impurities, and if the mean free path is much smaller than the distance between the impurities.